I believe you've won the "What the Heck is Going On With My Engine?!?" contest! Make sure and pull the spark plug for easier hand- spinning, and then VERIFY that:
1.) Spin the crank slowly forward...You should get (EXHAUST open/close) and then immediately afterward, (INTAKE open/close) and these events should take place every other complete turn of the crank. If it's not doing that, open the valve cover on top of the head and verify that the rockers are where they belong. Maybe one has slipped off of it's pivot and is actuating the other valve somehow, causing the double-tap. I've never pulled one of these motors apart yet, but that might be it. I had a Cadillac 425 rocker kinda slip off it's pivot, and similar things happened.